Question

$(217)_8$ is equivalent to

• A. \((6F)_{16}\)
• B. \((8E)_{16}\)
• C. \((8F)_{16}\)
• D. \((143)_{16}\)

Hint:

To convert base-8 to base-16, go via base-10 or group bits if preferred; remember hex values A–F.

Answer 1

The Correct Option is B

First, convert from octal to decimal: \[ (217)_8 = 2 \cdot 64 + 1 \cdot 8 + 7 = 128 + 8 + 7 = 143_{10} \] Now convert decimal to hexadecimal: \[ 143 \div 16 = 8 \text{ remainder } 15 \Rightarrow (8F)_{16} \] But 15 = E in hex, so the correct representation is \((8E)_{16}\)